When a pair of narrow-band filters with 3-nm bandwidth is utilized, the measured HOM interference in one DoF of polarization or OAM in Fig. REF (a) or (b) shows three dips at zero delay for the three Boson states and one peak at zero delay for the Fermion state. As shown in Fig. REF (c), the HOM interference in the polarization-OAM hyper-entangled states exhibits ten dips in nine Boson-Boson states (\(\lbrace \left|{\phi ^{+}} \right\rangle ,\left|{\phi ^{-}} \right\rangle ,\left|{\psi ^{+}} \right\rangle \rbrace \otimes \lbrace \left|{\mu ^{+}} \right\rangle ,\left|{\mu ^{-}} \right\rangle ,\left|{\nu ^{+}} \right\rangle \rbrace \) ) and one Fermion-Fermion state (\(\left|{\psi ^{-}} \right\rangle \otimes \left|{\nu ^{-}} \right\rangle \) ), and six peaks in three Boson-Fermion states (\(\lbrace \left|{\phi ^{+}} \right\rangle ,\left|{\phi ^{-}} \right\rangle ,\left|{\psi ^{+}} \right\rangle \rbrace \otimes \left|{\nu ^{-}} \right\rangle \) ) and three Fermion-Boson states (\(\left|{\psi ^{-}} \right\rangle \otimes \lbrace \left|{\mu ^{+}} \right\rangle ,\left|{\mu ^{-}} \right\rangle ,\left|{\nu ^{+}} \right\rangle \rbrace \) , as the theoretical predictions. To characterize a HOM interference, we utilize the visibility defined as \(V_{dip} = 1 - C_{0}/C_{\infty }\)  (\(V_{peak} = C_{0}/C_{\infty } - 1\) ) for the dip (peak) [1]}, [2]}, where \(C_{0}\)  and \(C_{\infty }\)  are fitted counts at zero and infinite delays. The extracted visibilities of the HOM interference for the four Bell states in the single DoF of polarization or OAM ranges from \(0.975 \pm 0.005\)  to \(0.992 \pm 0.066\)  or \(0.957 \pm 0.068\)  to \(0.993 \pm 0.003\) ; while the HOM interference for the sixteen hyper-entangled states has the extracted visibilities ranging from \(0.902 \pm 0.071\)  to \(0.993 \pm 0.002\)  (see [3]} for details and the corresponding results with 8-nm filters).
